If this spell is countered, none of its effects occur. In particular, it will go to the graveyard rather than to its owner’s library.

6/8/2016

If Green Sun’s Zenith is countered, none of its effects will happen. Notably, it will be put into its owner’s graveyard rather than shuffled into its owner’s library.

6/8/2016

In most cases, if you own Green Sun’s Zenith and cast it, you’ll shuffle your library twice. In practice, shuffling once is sufficient, but effects that care about you shuffling your library (like Psychogenic Probe, for example) will see that you’ve shuffled twice.

6/8/2016

If you own Green Sun’s Zenith, but an opponent casts it (due to Knowledge Pool’s effect, for example), that opponent searches his or her library for an appropriate creature card, then shuffles that library. That opponent then shuffles Green Sun’s Zenith into your library. You won’t shuffle any library in this case.